86 research outputs found
A higher-order active contour model of a `gas of circles' and its application to tree crown extraction
Many image processing problems involve identifying the region in the image
domain occupied by a given entity in the scene. Automatic solution of these
problems requires models that incorporate significant prior knowledge about the
shape of the region. Many methods for including such knowledge run into
difficulties when the topology of the region is unknown a priori, for example
when the entity is composed of an unknown number of similar objects.
Higher-order active contours (HOACs) represent one method for the modelling of
non-trivial prior knowledge about shape without necessarily constraining region
topology, via the inclusion of non-local interactions between region boundary
points in the energy defining the model. The case of an unknown number of
circular objects arises in a number of domains, e.g. medical, biological,
nanotechnological, and remote sensing imagery. Regions composed of an a priori
unknown number of circles may be referred to as a `gas of circles'. In this
report, we present a HOAC model of a `gas of circles'. In order to guarantee
stable circles, we conduct a stability analysis via a functional Taylor
expansion of the HOAC energy around a circular shape. This analysis fixes one
of the model parameters in terms of the others and constrains the rest. In
conjunction with a suitable likelihood energy, we apply the model to the
extraction of tree crowns from aerial imagery, and show that the new model
outperforms other techniques
Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.
The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics.
This approach is based on defining new mathematical representations of parameterized surfaces, including the square root normal field (SRNF), and then using the L2 norm to compare their shapes. Past work is based on using the pullback of the L2 metric to the space of surfaces, performing statistical analysis under this induced Riemannian metric. However, if one can estimate the inverse of the SRNF mapping, even approximately, a very efficient framework results: the surfaces, represented by their SRNFs, can be efficiently analyzed using standard Euclidean tools, and only the final results need be mapped back to the surface space. Here we describe a procedure for inverting SRNF maps of star-shaped surfaces, a special case for which analytic results can be obtained. We test our method via the classification of 34 cases of ADHD (Attention Deficit Hyperactivity Disorder), plus controls, in the Detroit Fetal Alcohol and Drug Exposure Cohort study. We obtain state-of-the-art results
Structured prior distributions for the covariance matrix in latent factor models
Factor models are widely used for dimension reduction in the analysis of
multivariate data. This is achieved through decomposition of a p x p covariance
matrix into the sum of two components. Through a latent factor representation,
they can be interpreted as a diagonal matrix of idiosyncratic variances and a
shared variation matrix, that is, the product of a p x k factor loadings matrix
and its transpose. If k << p, this defines a sparse factorisation of the
covariance matrix. Historically, little attention has been paid to
incorporating prior information in Bayesian analyses using factor models where,
at best, the prior for the factor loadings is order invariant. In this work, a
class of structured priors is developed that can encode ideas of dependence
structure about the shared variation matrix. The construction allows
data-informed shrinkage towards sensible parametric structures while also
facilitating inference over the number of factors. Using an unconstrained
reparameterisation of stationary vector autoregressions, the methodology is
extended to stationary dynamic factor models. For computational inference,
parameter-expanded Markov chain Monte Carlo samplers are proposed, including an
efficient adaptive Gibbs sampler. Two substantive applications showcase the
scope of the methodology and its inferential benefits
Bayesian shape modelling of cross-sectional geological data.
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is therefore of some interest, but current classifications are simplistic and ad hoc. In this paper, we describe the first steps towards a coherent statistical analysis of these shapes by deriving the integrated likelihood for data shapes given class parameters. The result is of interest beyond this particular application
Modality-Constrained Density Estimation via Deformable Templates
Estimation of a probability density function (pdf) from its samples, while satisfying certain shape constraints, is an important problem that lacks coverage in the literature. This article introduces a novel geometric, deformable template constrained density estimator (dtcode) for estimating pdfs constrained to have a given number of modes. Our approach explores the space of thus-constrained pdfs using the set of shape-preserving transformations: an arbitrary template from the given shape class is transformed via a shape-preserving transformation to obtain the final optimal estimate. The search for this optimal transformation, under the maximum-likelihood criterion, is performed by mapping transformations to the tangent space of a Hilbert sphere, where they are effectively linearized, and can be expressed using an orthogonal basis. This framework is first applied to (univariate) unconditional densities and then extended to conditional densities. We provide asymptotic convergence rates for dtcode, and an application of the framework to the speed distributions for different traffic flows on Californian highways
A phase field method for tomographic reconstruction from limited data.
Classical tomographic reconstruction methods fail for problems in which there is
extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal
mass ejections (CMEs), a space weather phenomenon with potential negative effects on
the Earth, is one such problem. However, the topological complexity of CMEs renders
recent limited data reconstruction methods inapplicable. We propose an energy function,
based on a phase field level set framework, for the joint segmentation and tomographic
reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar
telescope. Our phase field model deals easily with complex topologies, and is more
robust than classical methods when the data are very sparse. We use a fast variational
algorithm that combines the finite element method with a trust region variant of Newton’s
method to minimize the energy. We compare the results obtained with our model to
classical regularized tomography for synthetic CME-like images
Texture-adaptive mother wavelet selection for texture analysis
We discuss the use of texture-adaptive mother wavelets in an adaptive probabilistic wavelet packet approach to texture analysis. First, we present the use of adaptive biorthogonal wavelet packet bases in such ananalysis, thus combining the advantages of biorthogonal wavelets (FIR,linearphase) with those of a coherent texture model. In this case, the computation of the probability uses both the primal and dual coefficient of the adapted biorthogonal wavelet packet basis. The computation of the biorthogonal wavelet packet coefficient is done using a lifting scheme, which is very efficien in terms of reducing the computational complexity and achieving an intrinsic parameterization of wavelet filters Then we include the mother wavelet parameter into this model, in order to fin the optimal mother wavelet for a given texture using this model. The model is applied to the classificatio of mosaics of Brodatz textures, the results showing improvement over the performance of the corresponding orthogonal wavelets
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